Can a dog get a cold from going from warm inside to staying in the colder outside?

The simple answer is "no" -- dogs, and humans as well, do not contract illnesses merely by spending time outdoors in cold weather. However, if the dog is spending time with other, unfamiliar dogs or in unfamiliary territory where diseased feces, etc., may be present, your dog could conceivably end up with, among other things, kennel cough, Valley Fever, parvovirus -- unless he/she is vaccinated against such diseases.

That said, depending on your climate, it's never a great idea to leave a dog out in snowy, rainy, or severely cold (or hot, for that matter, for other reasons) weather for long periods of time. There are a few reasons for this, the first being that dogs, like humans, can develop frostbite and hypothermia. Dogs are social creatures, and to be cast out of the family like an unwanted cockroach can potentially cause behavioral issues down the road.